Andy Murray has capped a year in which he broke a 77-year Wimbledon hoodoo and played his way into the hearts of the nation by winning the BBC's Sports Personality of the Year award.

The Scot was the shortest priced favourite in the 60 years of the prize, despite another stellar sporting year that included a British victory in the Tour de France, a home Ashes victory and the first British and Irish Lions victory overseas for 16 years.

Murray was shown accepting the award from Martina Navratilova via a live video link to Miami, where he is training as he recuperates from back surgery.

"Winning something like Wimbledon is something I've dedicated a lot of years towards and winning something like this is an acknowledgement of your achievement from the British public," he said afterwards.

Welsh rugby player Leigh Halfpenny, who was man of the series in the British and Irish Lions victory in Australia, came second and jockey AP McCoy, who this year rode his 4,000th winner and who won the prize in 2010, came third. But both said afterwards there could only have been one winner.

A "very, very proud" Murray had agonised over whether to attend the ceremony in Leeds but, displaying the drive and dedication that has taken him to the top of his sport in a golden era of men's tennis, instead opted to remain at his training camp.

He will train every day up to Boxing Day, including Christmas Day, when he will fly to Abu Dhabi to play Jo-Wilfried Tsonga in a bid to be fit for next month's Australian Open.

"The easy decision would have been to have come over and I would have loved it and had a great time," said Murray, who defeated Novak Djokovic on a hot day in July to seal the Wimbledon title.

"I would have rather been there than running around a tennis court for three hours. But it was the right decision for my career and my back and my preparations for Australia and that's why the decision was made."

The Scot was the shortest-priced favourite in the 60-year history of the prize, despite a year that included a British victory in the Tour de France, a home Ashes series victory and the first British and Irish Lions victory overseas for 16 years. The bookmakers were proved right as Murray won with 56% of the vote.

After his tears in defeat to Roger Federer in 2012, a subsequent Olympic gold on Centre Court and an affecting eve of tournament BBC documentary, 2013 was widely seen as the year in which Murray won the hearts of the British public after a sometimes awkward courtship.

The documentary undoubtedly helped, he said, adding: "The support I got at Wimbledon this year was by far the best I had ever had. None of the others I'd played could compare to this one."

Accepting the prize, he joked about his inability to convey his emotions: "No matter how excited I try to sound my voice still sounds incredibly boring. But I'm really excited right now."

Asked whether he could retain his Wimbledon title in 2014 he said: "I'll give it everything I've got. I had unbelievable support at Wimbledon this year, if I get the support behind me I know I'll have a chance."

As she left the arena in Leeds, his mother Judy would have seen a huge advert from his sponsor Adidas bearing the slogan: "Not bad for a man with no personality."

Murray took his place on a 10-strong shortlist that also included Tour de France winner Chris Froome, sailor Ben Anslie, who helped Team Oracle recover from an 8-1 deficit to win the America's Cup, and Mo Farah, who won double gold at the world championships in Moscow, a year after doing the same at the London Olympics.

The other nominees were McCoy, cricketer Ian Bell, wheelchair sprinter Hannah Cockroft, Halfpenny, world 400m champion Christine Ohuruogu and golfer Justin Rose, who became the first Englishman to win the US Open for 43 years.

Murray was 25-1 on with most bookmakers by the time the live BBC1 show started, with McCoy second favourite at 16-1 and Farah 28-1.

The bookmakers were proved right after Murray cantered to victory. With viewers able to make their choice online as well as by phone for the first time, there was expected to be a record number of votes cast.

After returning to London last year for an glut of post-Olympics nostalgia, the BBC continued their policy of taking the show on the road in front of 12,000 spectators at the First Direct Arena in Leeds. But they had to make do without the presence of Murray, Rose or Farah – who were all training or competing abroad.

During the show, an emotional Ainslie paid tribute to his late friend Andrew "Bart" Simpson who was killed in an accident in the runup to the America's Cup.

"I think most of us would agree that sportsmen and women are pretty single-minded people. He was the one person who had some perspective on life. He taught us a lot of lessons in life as well as in death."

Despite previously winning the lifetime achievement prize in 2001, after he first announced his retirement – before performing a U-turn – Sir Alex Ferguson was given a special "Diamond award" to mark 60 years of the programme.

Team of the year went to the Lions in recognition of their 2-1 series victory in Australia and Warren Gatland, who masterminded their victory, picked up the Coach of the Year prize.

Red Bull's Sebastian Vettel, who won his fourth consecutive Formula One world title in 2013, was named Overseas Sports Personality of the Year.

Skeet shooter Amber Hill, who was 15 when she became the youngest winner of a senior World Cup event this year, won the Young Sports Personality of the Year award. Murray himself had won that award in 2004.

The Helen Rollason award, named after the late BBC presenter and awarded for outstanding achievement in the face of adversity, was awarded posthumously to Anne Williams for her tireless campaigning on behalf of her son Kevin, who was one of 96 football fans who died at Hillsborough in April 1989.

Williams, who died in April this year, lived long enough to see the publication of the Hillsborough Independent Panel report, which exonerated Liverpool fans and revealed the scale of the establishment coverup to protect the police and authorities, and the high court decision to quash the original verdicts and order a new inquest.

Former Liverpool captain Alan Hansen presented the award to her daughter Sara, son Michael and brother Danny to a standing ovation from the crowd following a moving citation by actress Sue Johnston.

• The standfirst of this article was corrected on Sunday 15 December 2013 because it stated that Andy Murray was the first Briton to win Wimbledon since 1936. Virgina Wade won the women's singles championship at Wimbledon in 1977.